9x2 +9x +5
3x-2 ) 27x3 +9x2 -3x-10
27x3-18x2
27x2-3x
27x2-18x
15x-10
15x-10
0
ANSWER: 9x2 +9x +5.
The question in the title needs to be clarified to resolve ambiguities in the wording.
A possible interpretation is:
[x4/(x3+7x2)]-[(6x+8)/(x-2)],
[x2/(x+7)]-[(6x+8)/(x-2)], (the parentheses clarify the meaning)
(x2(x-2)-(6x+8)(x+7))/((x+7)(x-2)),
(x3-2x2-6x2-50x-56)/((x+7)(x-2)),
(x3-8x2-50x-56)/(x2+5x-14). Now the long algebraic division:
x - 13 (quotient)
x2+5x-14 ) x3-8x2 -50x - 56
x3+5x2-14x
-13x2-36x - 56
-13x2-65x+182
29x-238 (remainder)
Several other interpretations are possible.